Details

Time bar (total: 2.3m)

sample4.2s

Algorithm
intervals
Results
4.0s921×body10240exit
74.0ms256×body80valid

simplify317.0ms

Calls
1 calls:
Slowest
316.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

25.1b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.3b
(* y.re (log (hypot x.re x.im)))
0.2b
(* (atan2 x.im x.re) y.im)
0.2b
(* (atan2 x.im x.re) y.re)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow fma-udef
Calls
4 calls:
Slowest
12.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* y.re (log (hypot x.re x.im)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series312.0ms

Calls
4 calls:
Slowest
163.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
103.0ms
(* y.re (log (hypot x.re x.im)))
26.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)

simplify2.0s

Calls
48 calls:
Slowest
333.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
330.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
326.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
325.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
145.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
52×hypot-def
32×*-un-lft-identity
24×swap-sqr
21×*-commutative unswap-sqr
16×sqrt-prod
14×associate-*l*
10×pow1 distribute-lft-out
8×add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×+-commutative sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square cos-sum flip3-+ flip-+
1×pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
92.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

series464.0ms

Calls
4 calls:
Slowest
206.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
136.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.5s

Calls
78 calls:
Slowest
336.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
323.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
311.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
299.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
276.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune2.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes284.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch3.0ms

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30262×body10240exit
3.7s8000×body80valid